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Zero-point energy is the energy of the vacuum. Disturbing the vacuum results in a change in the zero-point energy. In 1948, Casimir considered the change in the zeropoint energy when the vacuumis disturbed by two parallelmetal plates. The plates disturb the vacuum by restricting the quantum fluctuations of the electromagnetic field. Casimir found that the change in the zero-point energy implies that the plates are attracted to each other. With the recent advances made in the experimental verification of this remarkable result, theoretical interest has been rekindled. In addition to the original parallel plate configuration, several other boundaries have been studied. In this thesis, two novel boundaries are considered: elliptic-cylindrical and spheroidal. The results for these boundaries lead to the conjecture that zero-point energy does not change for small deformations of the boundary that preserve volume. Assuming the conjecture, it is shown that zero-point energy plays a stabilizing role in quantum chromodynamics, the leading theory of the strong interaction.

In this thesis I consider the general problem of how to make the best possible phase measurements using feedback. Both the optimum input state and optimum feedback are considered for both single-mode dyne measurements and two-mode interferometric measurements. I derive the optimum input states under general dyne measurements when the mean photon number is fixed, both for general states and squeezed states. I propose a new feedback scheme that introduces far less phase uncertainty than mark II feedback, and is very close to the theoretical limit. I also derive results for the phase variance when there is a time delay in the feedback loop, showing that there is a lower limit to the introduced phase variance, and this is approached quite accurately under some conditions. I derive the optimum input states for interferometry, showing that the phase uncertainty scales as 1/N for all the common measures of uncertainty. This is contrasted with the |j0> state, which does not scale as 1/N for all measures of phase uncertainty. I introduce an adaptive feedback scheme that is very close to optimum, and can give scaling very close to 1/N for the uncertainty. Lastly I consider the case of continuous measurements, for both the dyne and interferometric cases.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.